Question
Find the slope and \( y \)-intercept of the following linear equation. Express the \( y \)-intercept as a coordinate pair. \[ y=\frac{1}{5} x \] Answer
Ask by Hammond Curry. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The slope is \( \frac{1}{5} \) and the \( y \)-intercept is \( (0, 0) \).
Solution
To identify the slope and \( y \)-intercept of the linear equation:
\[
y = \frac{1}{5}x
\]
we can compare it to the standard slope-intercept form of a linear equation:
\[
y = mx + b
\]
where:
- \( m \) is the **slope** of the line.
- \( b \) is the **\( y \)-intercept**, expressed as a coordinate pair \((0, b)\).
**Step-by-Step Breakdown:**
1. **Identify the Slope (\( m \)):**
In the given equation, \( y = \frac{1}{5}x \), the coefficient of \( x \) is \( \frac{1}{5} \).
\[
\text{Slope } (m) = \frac{1}{5}
\]
2. **Determine the \( y \)-Intercept (\( b \)):**
The equation \( y = \frac{1}{5}x \) does not have a constant term, which implies that \( b = 0 \).
Therefore, the \( y \)-intercept is at the point where \( x = 0 \):
\[
y = \frac{1}{5}(0) = 0
\]
\[
\text{\( y \)-intercept} = (0, 0)
\]
**Final Answer:**
- **Slope:** \( \frac{1}{5} \)
- **\( y \)-intercept:** \( (0,\,0) \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
The slope of the equation \( y = \frac{1}{5} x \) is \( \frac{1}{5} \). This means that for every 1 unit increase in \( x \), \( y \) increases by \( \frac{1}{5} \) units. The \( y \)-intercept is the point where the line crosses the \( y \)-axis, which occurs when \( x = 0 \). Plugging \( x = 0 \) into the equation gives us \( y = \frac{1}{5}(0) = 0 \). Thus, the \( y \)-intercept as a coordinate pair is \( (0, 0) \).
